#25 Correction of Exchange-Correlation Error (2): Van der Waals Correction - It's Over 9000!


#25 Correction of Exchange-Correlation Error (2): Van der Waals Correction

2019-11-28 19:04:00
In the previous weekly tip, we learned about DFT+U among the three exchange-correlation energy correction methods. In this weekly tip, we will study the van der Waals correction.

 

1. Van der Waals interaction

Van der Waals force, which is also called the dispersive interaction, is the weak interaction that occurs among temporarily induced dipoles caused by the fluctuation of electron density. Every material has van der Waals force [1].

Furthermore, Van der Waals force needs correction because the GGA functional, which is the semi-local functional, could not describe the long-range interaction [2].

Moreover, Van der Waals force can be corrected through two methods, using the empirical interatomic van der Waals parameter or van der Waals functional.

The first method contains the DFT+D method, which corrects the interatomic interaction between the two atoms [3]. The DFT+D3 method adds an interatomic interaction among three atoms to the DFT+D method [4]. Furthermore, the DFT+D method obtains the dispersion energy empirically, in which the value depends on the kind of model [3].

As the second correction method, the van der Waals functional method is calculated using specific functional, which is made considering the van der Waals interaction. This specific functional is vdW-DF [5], etc.

 

Van der Waals correction can apply to the system have weak bonding majorly. It is well known that it is better applying van der Waals correction when performing calculation for the bonding between nonpolarized molecules such as benzene, or for the weak binding system like hydrogen bonding system. Also, considering van der Waals interaction is better for physisorption of molecule, the phase change memory material GST, IST, or 2D layer materials graphite, TMD (ex. MoS2), MXene.
 

2. Setting the van der Waals correction in MatSQ

Van der Waals correction option can be added in the “Option” section (“Correction” changes into “Option”) at the Scripting Option: Template.



Select the van der Waals option to add van der Waals correction keywords. You can choose some of the options, which are DFT+D [3], DFT+D3 [4], Tkatchenko-Scheffler [6], and XDM [7]. The commonly used methods are DFT+D and DFT+D3.

 

 

3. Calculation Results with van der Waals Correction

In this example, we check the effect of the van der Waals correction by calculating the interlayer distance of graphite, where the van der Waals interaction mainly behaves.



 

The following figure compares the PBE calculation results with the van der Waals correction results, which uses the DFT+D3 method.



 

The most stable interlayer distance can be acquired by fitting the energy of the graphite obtained for several interlayer distances. In this example, the cubic spline fitting method was used to determine the stable interlayer distance.



ApproachInterlayer distance (Å)Binding energy (meV/atom)
PBE4.335-1.994
Van der Waals correction (DFT+D3) 3.510-40.69
Experiment 3.336 [8]

 

👉 Click to see the calculation results


 

For the graphite with any correction, the most stable interlayer distance is calculated as 4.335 Å. However, for the graphite with the van der Waals correction through the DFT+D3 option, the most stable interlayer distance is calculated as 3.336 Å. On the other hand, the experimental measurement of the graphite’s interlayer distance is 3.336 Å. Because of this, the error in the calculation result decreased when the van der Waals correction is applied.

Furthermore, we obtained the graphite’s binding energy by calculating the energy difference between graphite and graphene. The binding energy is calculated as 41 meV per atom when the van der Waals correction is being applied. It means that if the van der Waals correction is applied, then the graphite is stabilized energetically than the graphene by using the van der Waals force.

Similar to these results, the van der Waals interaction behaves between the layers in 2D materials, so the van der Waals correction needed to obtain appropriate results.

 

In this weekly tip, we learned how to correct the van der Waals interactions, which are long-range interactions under a semi-local functional. The van der Waals correction is essential, specifically for systems wherein the effectiveness of the van der Waals interactions is important.

In MatSQ, you can add the van der Waals correction to your calculation easily by checking the van der Waals checkbox.

Obtain your DFT results with van der Waals correction using Materials Square!
 




[1] Smith, J. G. (2014). Organic Chemistry, 4th Edition.
[2] Wu, Q., & Yang, W. (2002). Empirical correction to density functional theory for van der Waals interactions. The Journal of chemical physics116(2), 515-524.
[3] Grimme, S. (2004). Accurate description of van der Waals complexes by density functional theory including empirical corrections. Journal of computational chemistry25(12), 1463-1473.
[4] Grimme, S., Antony, J., Ehrlich, S., & Krieg, H. (2010). A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of chemical physics132(15), 154104.
[5] Dion, M., Rydberg, H., Schröder, E., Langreth, D. C., & Lundqvist, B. I. (2004). Van der Waals density functional for general geometries. Physical review letters, 92(24), 246401.
[6] Tkatchenko, A., & Scheffler, M. (2009). Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Physical review letters, 102(7), 073005.
[7] Becke, A. D., & Johnson, E. R. (2007). Exchange-hole dipole moment and the dispersion interaction revisited. The Journal of chemical physics, 127(15), 154108.; Otero-de-la-Roza, A., & Johnson, E. R. (2012). Van der Waals interactions in solids using the exchange-hole dipole moment model. The Journal of chemical physics, 136(17), 174109.
[8] Chen, X., Tian, F., Persson, C., Duan, W., & Chen, N. X. (2013). Interlayer interactions in graphites. Scientific reports, 3, 3046.

 

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